model to keep q>1 in stationary transport

[jmcclena]

This pull request implements Jardin's model for stationary sawteeth to raise q>1.

Example run

using Revise
using FUSE
ini, act = FUSE.case_parameters(:D3D)


# Initialize the `dd` structure with 0D parameters
dd = FUSE.init(ini, act);
dd_init = deepcopy(dd)
#act.ActorStationaryPlasma.convergence_error = 0.05#1e-8
act.ActorStationaryPlasma.max_iter = 5
FUSE.ActorStationaryPlasma(dd,act)

[jmcclena]

@bclyons12 Do you know if eta needs to be updated in the dd to get the correct flux consumption?

[bclyons12]

I do not. I'd just have to look at how and wear the flux consumption is calculated.

I'll look this over next week.

[orso82]

@jmcclena I wonder if we could extend this to time-dependent QED, using the q-profile at the previous time-slice to inform if the conductivity profile should be flattened.

[jmcclena]

@orso82

For time-dependent, I think it might be better to flatten the profiles directly like this:

function flatten(prof, rad, vol, width, i_inversion)
    prof_tanh = 0.5 .* tanh.(-(rad .- rad[i_inversion]) ./ width) .+ 0.5

    en = IMAS.integrate(vol, prof)
    en_tanh = IMAS.integrate(vol,prof_tanh)
    prof_cut = deepcopy(prof)
    prof_cut[1:i_inversion] .= prof_cut[i_inversion]
    en_cut = IMAS.integrate(vol,prof_cut)

    prof_new = prof_cut .+ (en .- en_cut) ./ en_tanh .* prof_tanh

    return prof_new
end

Then we can flatten the profiles based on some condition (say q0<0.9) on the Jt step, taking half steps of the temperature/density profiles to keep things in sync.

[orso82]

@jmcclena @bclyons12 looking more into this, what should happen to the non-inductive current inside of the inversion radius? I wonder if that non-inductive current get redistributed inside the inversion radius, perhaps using the same flatten() function that @jmcclena proposed?

[bclyons12]

I know that bootstrap current relaxes on the electron collision time, though I'm not sure what happens if there's large MHD that's redistributing particles anyway. Nor do I know how other noninductive sources should behave.